Question

A particular rsistance wire has a resistance of 3.0 ohm per metre. Find:
(a) The total resistance of three lengths of this wire each 1.5 m long, joined in parallel.
(b) The potential difference of the battery which gives a current of 2.0 A in each of the 1.5 m length when connected in parallel to the battery (assume that the resistance of battery is negligible).
(c) The resistance of 5 m length of a wire of the same material, but with twice the area of cross-section.

Answer 1

(a) Resistance of 1 m of wire = 3 $\Omega$
Resistance of 1.5 m of wire = 3 × 1.5 = 4.5 $\Omega$

(b) I = 2 A

V = IR = 2 × 4.5 = 9 V

(c) R = 3 ohm for 1 m

For 5 m, R = 3 × 5 = 15 ohm

But, cross-sectional area is double and we know that the resistance is inversely proportional to area.

So, new resistance = 15/2 = 7.5 ohm